Parallel Newton-Krylov-Schwarz Algorithms for the Transonic Full Potential Equation.

Abstract

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two/level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1996
Accession Number
ADA314236

Entities

People

  • David E. Keye
  • David P. Young
  • Robin G. Melvin
  • William D. Gropp
  • Xiao-chuan Cai

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Contracts
  • Differential Equations
  • Engineering
  • Equations
  • Fluid Flow
  • Geometry
  • Linear Systems
  • Mach Number
  • Nonlinear Algebraic Equations
  • Numbers
  • Partial Differential Equations
  • Square Roots

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Parallel and Distributed Computing.

Technology Areas

  • Space